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A002668
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Continued cotangent for e.
(Formerly M1900 N0748)
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12
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OFFSET
| 1,1
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REFERENCES
| D. H. Lehmer, A cotangent analogue of continued fractions, Duke Math. J., 4 (1935), 323-340.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,11
Eric Weisstein's World of Mathematics, Lehmer Cotangent Expansion
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MATHEMATICA
| b[1] = E; b[n_] := b[n] = (b[n-1]*Floor[b[n-1]]+1) / (b[n-1]-Floor[b[n-1]]); a[n_] := Floor[b[n]]; Table[a[n], {n, 1, 8}] (* From Jean-François Alcover, Jan 17 2012, after Pari *)
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PROG
| (PARI) { default(realprecision, 10000); bn=vector(11); bn[1]=exp(1); for(n=2, 11, bn[n]=(bn[n-1]*floor(bn[n-1]) + 1)/(bn[n-1] - floor(bn[n-1]))); for (n=1, 11, write("b002668.txt", n, " ", floor(bn[n]))); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 04 2009]
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CROSSREFS
| Sequence in context: A064605 A132039 A204552 * A193205 A093062 A057984
Adjacent sequences: A002665 A002666 A002667 * A002669 A002670 A002671
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from J. O. Shallit.
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